Question: Convert $\rm{A}03_{16}$ to a base 10 integer, where the 'digits' A through F represent the values 10, 11, 12, 13, 14, and 15 in order.
In base 16, $A = 10$, $B = 11$, $C = 12$, $D = 13$, $E = 14$, and $F = 15$. So $A03 = 10\cdot16^2 + 0\cdot16 + 3 = \boxed{2563}.$